1. Technical Field
The present disclosure relates generally to the logging of subsurface formations surrounding a wellbore using a downhole logging tool, and particularly to determining when higher order processing of the logging measurements is advantageous or appropriate.
2. Background Art
Logging tools have long been used in wellbores to make, for example, formation evaluation measurements to infer properties of the formations surrounding the borehole and the fluids in the formations. Common logging tools include electromagnetic tools, nuclear tools, and nuclear magnetic resonance (NMR) tools, though various other tool types are also used. Early logging tools were run into a wellbore on a wireline cable, after the wellbore had been drilled. Modern versions of such wireline tools are still used extensively.
A 3D tri-axial induction tool can measure the nine-component apparent conductivity tensor (σm(i, j, k), j, k=1, 2, 3) at multiple spacings represented by the index i. FIG. 1 illustrates an exemplary prior art tri-axial array and associated measurement. Those measurements are usually obtained in the frequency domain by firing the transmitter with a continuous wave (CW) of a given frequency to enhance the signal-to-noise ratio. However, measurements of the same information content could also be obtained and used from time domain signals through a Fourier decomposition process. This stems from the well-known physics principle of frequency-time duality. Certain formation properties, such as horizontal and vertical conductivities (σh, σv), relative dip angle (θ), and the dip azimuthal direction (Φ), as well as borehole/tool properties, such as mud conductivity (σmud), hole diameter (hd), tool eccentering distance (decc), and tool eccentering azimuthal angle (ψ) affect the conductivity tensors. FIGS. 2A and 2B illustrate an eccentered tool in a borehole drilled through an anisotropic formation having a dip angle. In even a simplified model of a layered anisotropic formation traversed obliquely by a borehole, the response represented by the conductivity tensors depends on the above eight parameters (σh, σv, θ, Φ, σmud, hd, decc, ψ) in a very complicated manner. The effects of the borehole/tool on the measured conductivity tensors may be very big, even in an oil base mud (OBM) environment. However, through one or more inversion techniques, the above borehole/formation parameters can be calculated and the borehole effects removed from the measured conductivity tensor.
After borehole correction, the borehole corrected measurements can be further processed using a simplified model that does not contain a borehole. For example, one may employ a simple model of uniform anisotropic formation having an arbitrary dip angle with respect to the tool, as illustrated in FIGS. 3A and 3B. This is often referred to as a “zero-dimensional” (ZD) model because the modeled formation does not vary in the axial and radial directions of the tool. In the ZD model, the controlling parameters are formation horizontal (Rh) and vertical (Rv) resistivities, the relative dip angle (θ), and the dip azimuth angle (Φ). (Note, the resistivity is the reciprocal of the conductivity, so those terms are used somewhat interchangeably throughout this disclosure since knowing one makes it a simple matter to compute the other.) In a real-world logging environment, the formation properties are generally unknown. The simple ZD model is generally the most versatile processing model available to generate coarse estimates of formation properties over the well path.